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<div class="title">CalibVolSurfCCE.py</div>  </div>
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<div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">#!/usr/bin/python</span>
<a name="l00002"></a>00002 <span class="comment"># -*- coding: utf-8 -*-</span>
<a name="l00003"></a>00003 
<a name="l00004"></a>00004 <span class="comment"># Copyright (c) 2011</span>
<a name="l00005"></a>00005 <span class="comment">#</span>
<a name="l00006"></a>00006 <span class="comment"># Permission is hereby granted, free of charge, to any person obtaining a</span>
<a name="l00007"></a>00007 <span class="comment"># copy of this software and associated documentation files (the &quot;Software&quot;),</span>
<a name="l00008"></a>00008 <span class="comment"># to deal in the Software without restriction, including without limitation</span>
<a name="l00009"></a>00009 <span class="comment"># the rights to use, copy, modify, merge, publish, distribute, sublicense,</span>
<a name="l00010"></a>00010 <span class="comment"># and/or sell copies of the Software, and to permit persons to whom the</span>
<a name="l00011"></a>00011 <span class="comment"># Software is furnished to do so, subject to the following conditions:</span>
<a name="l00012"></a>00012 <span class="comment">#</span>
<a name="l00013"></a>00013 <span class="comment"># The above copyright notice and this permission notice shall be included in</span>
<a name="l00014"></a>00014 <span class="comment"># all copies or substantial portions of the Software.</span>
<a name="l00015"></a>00015 <span class="comment">#</span>
<a name="l00016"></a>00016 <span class="comment"># THE SOFTWARE IS PROVIDED &quot;AS IS&quot;, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR</span>
<a name="l00017"></a>00017 <span class="comment"># IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,</span>
<a name="l00018"></a>00018 <span class="comment"># FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE</span>
<a name="l00019"></a>00019 <span class="comment"># AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER</span>
<a name="l00020"></a>00020 <span class="comment"># LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,</span>
<a name="l00021"></a>00021 <span class="comment"># OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE</span>
<a name="l00022"></a>00022 <span class="comment"># SOFTWARE.</span>
<a name="l00023"></a>00023 <span class="comment">#</span>
<a name="l00024"></a>00024 <span class="comment"># Author: Jesus Carrero &lt;j.o.carrero@gmail.com&gt;</span>
<a name="l00025"></a>00025 <span class="comment"># Mountain View, CA</span>
<a name="l00026"></a>00026 
<a name="l00027"></a>00027 <span class="stringliteral">&quot;&quot;&quot; Calibrate volatility surface by means of Euler-Lagrange approach.</span>
<a name="l00028"></a>00028 <span class="stringliteral">    Please read the paper:</span>
<a name="l00029"></a>00029 <span class="stringliteral"></span>
<a name="l00030"></a>00030 <span class="stringliteral">&quot;&quot;&quot;</span>
<a name="l00031"></a>00031 
<a name="l00032"></a>00032 <span class="keyword">from</span> numpy <span class="keyword">import</span> c_, tile, meshgrid, zeros, ones, dot, asarray
<a name="l00033"></a>00033 <span class="keyword">from</span> scipy <span class="keyword">import</span> linalg
<a name="l00034"></a>00034 <span class="keyword">from</span> Poisson2DFiniteDifference <span class="keyword">import</span> Poisson2DFiniteDifference
<a name="l00035"></a>00035 <span class="keyword">from</span> scipy.sparse.linalg <span class="keyword">import</span> spsolve <span class="keyword">as</span> spsolve
<a name="l00036"></a>00036 <span class="keyword">from</span> itertools <span class="keyword">import</span> izip, count
<a name="l00037"></a>00037 
<a name="l00038"></a>00038 <span class="keyword">import</span> logging
<a name="l00039"></a>00039 <span class="keyword">import</span> pdb
<a name="l00040"></a>00040 
<a name="l00041"></a>00041 
<a name="l00042"></a>00042 <span class="keyword">class </span>CalibVolSurfCCE:<span class="comment">#(Poisson2DFiniteDifference):</span>
<a name="l00043"></a>00043 
<a name="l00044"></a>00044     <span class="stringliteral">&quot;&quot;&quot;</span>
<a name="l00045"></a>00045 <span class="stringliteral">    Algorithm:</span>
<a name="l00046"></a>00046 <span class="stringliteral">    1- Introduce a function. This will be the initial approximation to the true volatility.</span>
<a name="l00047"></a>00047 <span class="stringliteral">    2- At each point determine &#39;0 ?m?S; n?t?:</span>
<a name="l00048"></a>00048 <span class="stringliteral">    3- Use the Black-Scholes formula to approximate the load.</span>
<a name="l00049"></a>00049 <span class="stringliteral">    4- Use the values obtained in 3 to approximate.</span>
<a name="l00050"></a>00050 <span class="stringliteral">    5- Solve the Poisson equation</span>
<a name="l00051"></a>00051 <span class="stringliteral">    6- Take the function obtained in step 5 and call this &#39;1 : Repeat the above procedure</span>
<a name="l00052"></a>00052 <span class="stringliteral">       from step 3, using &#39;1 in place of &#39;0 to obtain the next approximation. Continue</span>
<a name="l00053"></a>00053 <span class="stringliteral">       until the di erence between successive iterates &#39;k and &#39;k+1 is smaller than some</span>
<a name="l00054"></a>00054 <span class="stringliteral">       desired tolerance.</span>
<a name="l00055"></a>00055 <span class="stringliteral">    &quot;&quot;&quot;</span>
<a name="l00056"></a>00056 
<a name="l00057"></a>00057     __slots__ = [<span class="stringliteral">&#39;m_price_grid&#39;</span>, <span class="stringliteral">&#39;m_time_grid&#39;</span>, <span class="stringliteral">&#39;m_strikes&#39;</span>, <span class="stringliteral">&#39;m_opt_prices&#39;</span>,
<a name="l00058"></a>00058                  <span class="stringliteral">&#39;m_int_rate&#39;</span>, <span class="stringliteral">&#39;m_sigma&#39;</span>, <span class="stringliteral">&#39;m_price_eng&#39;</span>, <span class="stringliteral">&#39;m_tol&#39;</span>, <span class="stringliteral">&#39;m_max_niter&#39;</span>,
<a name="l00059"></a>00059                  <span class="stringliteral">&#39;m_poiss_solver&#39;</span>]
<a name="l00060"></a>00060 
<a name="l00061"></a>00061     <span class="keyword">def </span><a class="code" href="classmodels_1_1CalibVolCurve_1_1CalibVolCurve.html#a8ed4e4cbabd0a3641f11c5959863462c">__init__</a>(self, one2dim=2):
<a name="l00062"></a>00062         <span class="stringliteral">&quot;&quot;&quot; instantiate an object of type volatility calibration.&quot;&quot;&quot;</span>
<a name="l00063"></a>00063 
<a name="l00064"></a>00064         (self.m_price_grid, self.m_time_grid) = (<span class="keywordtype">None</span>, <span class="keywordtype">None</span>)
<a name="l00065"></a>00065         (self.m_strikes, self.m_opt_prices, self.m_int_rate) = (<span class="keywordtype">None</span>, <span class="keywordtype">None</span>,
<a name="l00066"></a>00066                 <span class="keywordtype">None</span>)
<a name="l00067"></a>00067         (self.m_time2_mat, self.m_relax) = (<span class="keywordtype">None</span>, 1.0)
<a name="l00068"></a>00068         (self.m_sigma, self.m_price_eng, self.m_vega) = (<span class="keywordtype">None</span>, <span class="keywordtype">None</span>,
<a name="l00069"></a>00069                 <span class="keywordtype">None</span>)
<a name="l00070"></a>00070 
<a name="l00071"></a>00071         (self.m_tol, self.m_max_niter) = (1.0e-03, 100)
<a name="l00072"></a>00072         self.m_log_progress = logging.getLogger(<span class="stringliteral">&#39;CalibrateCCE&#39;</span>)
<a name="l00073"></a>00073         self.m_init_guesss = <span class="keywordtype">None</span>
<a name="l00074"></a>00074         self.m_load, self.m_time_posi, self.m_price_posi = <span class="keywordtype">None</span>, <span class="keywordtype">None</span>, <span class="keywordtype">None</span>
<a name="l00075"></a>00075 
<a name="l00076"></a>00076         self.m_one2dim = one2dim
<a name="l00077"></a>00077 
<a name="l00078"></a>00078         <span class="keywordflow">if</span> 2 == one2dim:
<a name="l00079"></a>00079             self.m_poiss_solver = Poisson2DFiniteDifference()
<a name="l00080"></a>00080         <span class="keywordflow">else</span>:
<a name="l00081"></a>00081             self.m_poiss_solver = <span class="keywordtype">None</span>
<a name="l00082"></a>00082 
<a name="l00083"></a>00083     <span class="keyword">def </span>set_simu_domain(self, leftx, botty, rightx, topy):
<a name="l00084"></a>00084         <span class="stringliteral">&quot;&quot;&quot; dirichlet boundary terms. &quot;&quot;&quot;</span>
<a name="l00085"></a>00085 
<a name="l00086"></a>00086         <span class="keyword">assert</span> 2 == self.m_one2dim
<a name="l00087"></a>00087         self.m_poiss_solver.set_simu_domain(leftx, botty, rightx, topy)
<a name="l00088"></a>00088 
<a name="l00089"></a>00089     <span class="keyword">def </span>set_bott_top(self, bott, top):
<a name="l00090"></a>00090         <span class="stringliteral">&quot;&quot;&quot; top bottom bc. &quot;&quot;&quot;</span>
<a name="l00091"></a>00091 
<a name="l00092"></a>00092         <span class="keyword">assert</span> 2 == self.m_one2dim
<a name="l00093"></a>00093         self.m_poiss_solver.set_bott_top(bott, top)
<a name="l00094"></a>00094 
<a name="l00095"></a>00095     <span class="keyword">def </span>set_xlxr(self, left, right):
<a name="l00096"></a>00096         <span class="stringliteral">&quot;&quot;&quot; left and right bc &quot;&quot;&quot;</span>
<a name="l00097"></a>00097 
<a name="l00098"></a>00098         self.m_poiss_solver.set_xlxr(left, right)
<a name="l00099"></a>00099 
<a name="l00100"></a>00100     <span class="keyword">def </span>set_dx_dy(self, delta_x, delta_y=0.):
<a name="l00101"></a>00101         <span class="stringliteral">&quot;&quot;&quot; granularity of the grid in x and y direction. &quot;&quot;&quot;</span>
<a name="l00102"></a>00102 
<a name="l00103"></a>00103         <span class="keywordflow">if</span> 2 == self.m_one2dim:
<a name="l00104"></a>00104             self.m_poiss_solver.set_dx_dy(delta_x, delta_y)
<a name="l00105"></a>00105 
<a name="l00106"></a>00106     <span class="keyword">def </span>set_calibration_data(self, strikes, time2_mat, prices):
<a name="l00107"></a>00107         <span class="stringliteral">&quot;&quot;&quot;</span>
<a name="l00108"></a>00108 <span class="stringliteral">            Calibation data is a triple of Strike Prices,</span>
<a name="l00109"></a>00109 <span class="stringliteral">            Time to Expiration and Observed Derivative prices.</span>
<a name="l00110"></a>00110 <span class="stringliteral">        &quot;&quot;&quot;</span>
<a name="l00111"></a>00111 
<a name="l00112"></a>00112         (self.m_strikes, self.m_time2_mat, self.m_opt_prices) = \
<a name="l00113"></a>00113             (asarray(strikes), asarray(time2_mat), asarray(prices))
<a name="l00114"></a>00114         self.m_strikes = self.m_strikes.reshape((self.m_strikes.size,
<a name="l00115"></a>00115                 1))
<a name="l00116"></a>00116         self.m_time2_mat = \
<a name="l00117"></a>00117             self.m_time2_mat.reshape((self.m_time2_mat.size, 1))
<a name="l00118"></a>00118         self.m_opt_prices = \
<a name="l00119"></a>00119             self.m_opt_prices.reshape((self.m_opt_prices.size, 1))
<a name="l00120"></a>00120 
<a name="l00121"></a>00121     <span class="keyword">def </span>set_interest_rate(self, interest_rate):
<a name="l00122"></a>00122         <span class="stringliteral">&quot;&quot;&quot; interest rate is assume constant in calibration. &quot;&quot;&quot;</span>
<a name="l00123"></a>00123 
<a name="l00124"></a>00124         self.m_int_rate = float(interest_rate)
<a name="l00125"></a>00125 
<a name="l00126"></a>00126     <span class="keyword">def </span>set_analytical_enginee(self, price_eng, vega=None):
<a name="l00127"></a>00127         <span class="stringliteral">&quot;&quot;&quot; set pricing engine, call, put, digital. Only one</span>
<a name="l00128"></a>00128 <span class="stringliteral">            allow in here. can be easyly extend to handle any engine.</span>
<a name="l00129"></a>00129 <span class="stringliteral">        &quot;&quot;&quot;</span>
<a name="l00130"></a>00130 
<a name="l00131"></a>00131         (self.m_price_eng, self.m_vega) = (price_eng, vega)
<a name="l00132"></a>00132 
<a name="l00133"></a>00133     <span class="keyword">def </span><a class="code" href="classmodels_1_1CalibBase_1_1CalibBase.html#ac435434054075cfced0f2f0ff74b9d5e">set_initial_guess</a>(self, init_guess):
<a name="l00134"></a>00134         <span class="stringliteral">&quot;&quot;&quot; assume volatility is constant to start with. &quot;&quot;&quot;</span>
<a name="l00135"></a>00135 
<a name="l00136"></a>00136         self.m_init_guesss = init_guess
<a name="l00137"></a>00137 
<a name="l00138"></a>00138     <span class="keyword">def </span>set_tol_and_niter(self, tol=1.0e-03, max_num_iter=100):
<a name="l00139"></a>00139         <span class="stringliteral">&quot;&quot;&quot; stopping criterias. &quot;&quot;&quot;</span>
<a name="l00140"></a>00140 
<a name="l00141"></a>00141         (self.m_tol, self.m_max_niter) = (tol, max_num_iter)
<a name="l00142"></a>00142 
<a name="l00143"></a>00143     <span class="keyword">def </span>set_relax_param(self, _lambda):
<a name="l00144"></a>00144         <span class="stringliteral">&quot;&quot;&quot; comming from Euler-Lagrange equations. &quot;&quot;&quot;</span>
<a name="l00145"></a>00145 
<a name="l00146"></a>00146         self.m_relax = float(_lambda)
<a name="l00147"></a>00147 
<a name="l00148"></a>00148     <span class="keyword">def </span>__set_up_calibration(self):
<a name="l00149"></a>00149         <span class="stringliteral">&quot;&quot;&quot; prepare everthing for  calibration. &quot;&quot;&quot;</span>
<a name="l00150"></a>00150 
<a name="l00151"></a>00151         <span class="keyword">assert</span> self.m_strikes.size == self.m_time2_mat.size
<a name="l00152"></a>00152         <span class="keyword">assert</span> self.m_strikes.size == self.m_opt_prices.size
<a name="l00153"></a>00153         <span class="keyword">assert</span> self.m_price_eng <span class="keywordflow">is</span> <span class="keywordflow">not</span> <span class="keywordtype">None</span>
<a name="l00154"></a>00154         <span class="keyword">assert</span> self.m_int_rate <span class="keywordflow">is</span> <span class="keywordflow">not</span> <span class="keywordtype">None</span>
<a name="l00155"></a>00155 
<a name="l00156"></a>00156         <span class="comment"># Initilize base engine</span>
<a name="l00157"></a>00157 
<a name="l00158"></a>00158         solver = self.m_poiss_solver
<a name="l00159"></a>00159         solver.set_up_engine()
<a name="l00160"></a>00160 
<a name="l00161"></a>00161         <span class="comment"># Computational grid</span>
<a name="l00162"></a>00162 
<a name="l00163"></a>00163         <span class="keywordflow">if</span> 2 == self.m_one2dim:
<a name="l00164"></a>00164             (self.m_price_posi, self.m_time_posi) = solver.get_indx_grid()
<a name="l00165"></a>00165             (self.m_price_grid, self.m_time_grid) = solver.get_mesh()
<a name="l00166"></a>00166         <span class="keywordflow">else</span>:
<a name="l00167"></a>00167             <span class="keyword">assert</span> <span class="keyword">False</span>
<a name="l00168"></a>00168 
<a name="l00169"></a>00169         <span class="comment"># Genereate initial guess</span>
<a name="l00170"></a>00170 
<a name="l00171"></a>00171         <span class="keywordflow">if</span> self.m_sigma <span class="keywordflow">is</span> <span class="keywordtype">None</span>:
<a name="l00172"></a>00172             (price_grid, time_grid) = (self.m_price_grid,
<a name="l00173"></a>00173                     self.m_time_grid)
<a name="l00174"></a>00174 
<a name="l00175"></a>00175             <span class="keyword">assert</span> self.m_init_guesss <span class="keywordflow">is</span> <span class="keywordflow">not</span> <span class="keywordtype">None</span>
<a name="l00176"></a>00176             self.m_sigma = self.m_init_guesss * ones((price_grid.size,
<a name="l00177"></a>00177                     time_grid.size), <span class="stringliteral">&#39;float&#39;</span>)
<a name="l00178"></a>00178             self.m_load = zeros(self.m_sigma.shape)
<a name="l00179"></a>00179             self.__update_discrete_load()
<a name="l00180"></a>00180 
<a name="l00181"></a>00181         solver.set_discrete_load(self.m_load)
<a name="l00182"></a>00182 
<a name="l00183"></a>00183     <span class="keyword">def </span>__price_contracts(self, posi_in_grid):
<a name="l00184"></a>00184         <span class="stringliteral">&quot;&quot;&quot; price derivatives base on current conditions. &quot;&quot;&quot;</span>
<a name="l00185"></a>00185 
<a name="l00186"></a>00186         prices = zeros(self.m_strikes.shape)
<a name="l00187"></a>00187         <span class="keywordflow">for</span> (i, k, t2mat) <span class="keywordflow">in</span> izip(count(), self.m_strikes,
<a name="l00188"></a>00188                               self.m_time2_mat):
<a name="l00189"></a>00189             (stock_price, k, t2mat) = ([self.m_price_grid[posi_in_grid[0]]],
<a name="l00190"></a>00190                     float(k), float(t2mat) - self.m_time_grid[posi_in_grid[1]])
<a name="l00191"></a>00191 
<a name="l00192"></a>00192             <span class="keywordflow">if</span> t2mat &lt;= 0:
<a name="l00193"></a>00193                 prices[i] = 0.
<a name="l00194"></a>00194                 <span class="keywordflow">continue</span>
<a name="l00195"></a>00195 
<a name="l00196"></a>00196             prices[i] = self.m_price_eng(stock_price, k, self.m_int_rate,
<a name="l00197"></a>00197                     self.m_sigma[posi_in_grid[0], posi_in_grid[1]], t2mat)
<a name="l00198"></a>00198         <span class="keywordflow">return</span> prices
<a name="l00199"></a>00199 
<a name="l00200"></a>00200     <span class="keyword">def </span>__vegas(self, posi_in_grid):
<a name="l00201"></a>00201         <span class="stringliteral">&quot;&quot;&quot;</span>
<a name="l00202"></a>00202 <span class="stringliteral">            Need to define a trust region for numerical derivatieves.</span>
<a name="l00203"></a>00203 <span class="stringliteral">            At this points is just at hoc</span>
<a name="l00204"></a>00204 <span class="stringliteral">        &quot;&quot;&quot;</span>
<a name="l00205"></a>00205 
<a name="l00206"></a>00206         vegas = zeros(self.m_strikes.shape)
<a name="l00207"></a>00207         <span class="keywordflow">for</span> (i, k, expiry) <span class="keywordflow">in</span> izip(count(), self.m_strikes,
<a name="l00208"></a>00208                 self.m_time2_mat):
<a name="l00209"></a>00209             (price_posi, strike, reduced_time) = \
<a name="l00210"></a>00210                 (self.m_price_grid[posi_in_grid[0]], float(k), float(expiry)
<a name="l00211"></a>00211                  - self.m_time_grid[posi_in_grid[1]])
<a name="l00212"></a>00212             <span class="keywordflow">if</span> reduced_time &lt;= 0:
<a name="l00213"></a>00213                 vegas[i] = 0.
<a name="l00214"></a>00214                 <span class="keywordflow">continue</span>
<a name="l00215"></a>00215 
<a name="l00216"></a>00216             vegas[i] = self.m_vega([price_posi], strike, self.m_int_rate,
<a name="l00217"></a>00217                                    self.m_sigma[posi_in_grid[0],
<a name="l00218"></a>00218                                    posi_in_grid[1]], reduced_time)
<a name="l00219"></a>00219         <span class="keywordflow">return</span> vegas
<a name="l00220"></a>00220 
<a name="l00221"></a>00221     <span class="keyword">def </span>__update_discrete_load(self):
<a name="l00222"></a>00222         <span class="stringliteral">&quot;&quot;&quot; assemble load as in the paper. &quot;&quot;&quot;</span>
<a name="l00223"></a>00223 
<a name="l00224"></a>00224         (xgrid, ygrid) = meshgrid(self.m_price_posi[1:-1],
<a name="l00225"></a>00225                                   self.m_time_posi[1:-1])
<a name="l00226"></a>00226 
<a name="l00227"></a>00227         <span class="keywordflow">if</span> 1 == self.m_one2dim:
<a name="l00228"></a>00228             (xgrid, ygrid) = (xgrid[0], ygrid[0])
<a name="l00229"></a>00229 
<a name="l00230"></a>00230         load = zeros( (xgrid.size, 1), <span class="stringliteral">&#39;float64&#39;</span>)
<a name="l00231"></a>00231         <span class="keywordflow">for</span> (i, posi_in_grid) <span class="keywordflow">in</span> izip(count(), c_[xgrid.flatten(),
<a name="l00232"></a>00232                              ygrid.flatten()]):
<a name="l00233"></a>00233             curr_val_minus_price = self.__price_contracts(posi_in_grid)
<a name="l00234"></a>00234             vegas = self.__vegas(posi_in_grid)
<a name="l00235"></a>00235             load[i] = self.m_relax * dot(vegas.T, curr_val_minus_price
<a name="l00236"></a>00236                     - self.m_opt_prices)
<a name="l00237"></a>00237 
<a name="l00238"></a>00238         (nypnts, nxpnts) = xgrid.shape
<a name="l00239"></a>00239 
<a name="l00240"></a>00240         self.m_load[1:-1, 1:-1] = -tile(load[0: nxpnts], (nypnts, 1)).reshape((nypnts, nxpnts))
<a name="l00241"></a>00241         <span class="comment">#self.m_load[1:-1, 1:-1] = load.reshape((nypnts, nxpnts))</span>
<a name="l00242"></a>00242 
<a name="l00243"></a>00243     <span class="keyword">def </span><a class="code" href="classmodels_1_1CalibVolCurve_1_1CalibVolCurve.html#a88db3b2fa23a03999527b6325be4ea85">calibrate</a>(self):
<a name="l00244"></a>00244         <span class="stringliteral">&quot;&quot;&quot; calibrate model. &quot;&quot;&quot;</span>
<a name="l00245"></a>00245 
<a name="l00246"></a>00246         self.__set_up_calibration()
<a name="l00247"></a>00247 
<a name="l00248"></a>00248         <span class="comment"># Calibration loop</span>
<a name="l00249"></a>00249 
<a name="l00250"></a>00250         solver = self.m_poiss_solver
<a name="l00251"></a>00251         (M, rhs) = solver.discretize()
<a name="l00252"></a>00252 
<a name="l00253"></a>00253         (nxpts, nypts) = (self.m_price_grid.size, self.m_time_grid.size)
<a name="l00254"></a>00254 
<a name="l00255"></a>00255         (vbott, vtop, vleft, vright) = solver.get_discretized_bc()
<a name="l00256"></a>00256 
<a name="l00257"></a>00257         <span class="stringliteral">&quot;&quot;&quot;</span>
<a name="l00258"></a>00258 <span class="stringliteral">        current_load = solver.post_process(nxpts, nypts,</span>
<a name="l00259"></a>00259 <span class="stringliteral">                                   vbott, vtop, vleft, vright,</span>
<a name="l00260"></a>00260 <span class="stringliteral">                                   self.m_load[1: -1, 1 :-1])</span>
<a name="l00261"></a>00261 <span class="stringliteral"></span>
<a name="l00262"></a>00262 <span class="stringliteral">        return (self.m_price_grid, self.m_time_grid, current_load)</span>
<a name="l00263"></a>00263 <span class="stringliteral">        &quot;&quot;&quot;</span>
<a name="l00264"></a>00264 
<a name="l00265"></a>00265         (nxp, nyp) = (int(nxpts - 2), int(nypts - 2))
<a name="l00266"></a>00266 
<a name="l00267"></a>00267         (error, iter_num) = (1000.0, 0)
<a name="l00268"></a>00268         <span class="keywordflow">while</span> iter_num &lt; self.m_max_niter:
<a name="l00269"></a>00269             updated_sigma = spsolve(M, rhs)
<a name="l00270"></a>00270 
<a name="l00271"></a>00271             <span class="comment"># compute error</span>
<a name="l00272"></a>00272 
<a name="l00273"></a>00273             error_new = linalg.norm(updated_sigma - self.m_sigma[1:-1,
<a name="l00274"></a>00274                                     1:-1].flatten())
<a name="l00275"></a>00275             <span class="keywordflow">if</span> abs(error_new - error) &lt; self.m_tol:
<a name="l00276"></a>00276                 <span class="keywordflow">break</span>
<a name="l00277"></a>00277             <span class="keywordflow">else</span>:
<a name="l00278"></a>00278                 error = error_new
<a name="l00279"></a>00279             <span class="keywordflow">print</span> <span class="stringliteral">&quot; current error. &quot;</span>, error
<a name="l00280"></a>00280 
<a name="l00281"></a>00281             <span class="comment"># update sigma</span>
<a name="l00282"></a>00282 
<a name="l00283"></a>00283             self.m_sigma[1:-1, 1:-1] = updated_sigma.reshape(nyp,
<a name="l00284"></a>00284                     nxp).T.copy()
<a name="l00285"></a>00285 
<a name="l00286"></a>00286             <span class="comment"># compute the new load vector.</span>
<a name="l00287"></a>00287 
<a name="l00288"></a>00288             self.__update_discrete_load()
<a name="l00289"></a>00289             solver.set_discrete_load(self.m_load)
<a name="l00290"></a>00290             <span class="stringliteral">&quot;&quot;&quot;</span>
<a name="l00291"></a>00291 <span class="stringliteral">            current_load = solver.post_process(nxpts, nypts,</span>
<a name="l00292"></a>00292 <span class="stringliteral">                                   vbott, vtop, vleft, vright,</span>
<a name="l00293"></a>00293 <span class="stringliteral">                                   self.m_load[1: -1, 1 :-1])</span>
<a name="l00294"></a>00294 <span class="stringliteral"></span>
<a name="l00295"></a>00295 <span class="stringliteral">            return (self.m_price_grid, self.m_time_grid, current_load)</span>
<a name="l00296"></a>00296 <span class="stringliteral">            &quot;&quot;&quot;</span>
<a name="l00297"></a>00297             <span class="comment"># recompute rhs.</span>
<a name="l00298"></a>00298 
<a name="l00299"></a>00299             rhs = solver.get_rhs()
<a name="l00300"></a>00300             iter_num = iter_num + 1
<a name="l00301"></a>00301 
<a name="l00302"></a>00302         solu = solver.post_process(nxpts, nypts,
<a name="l00303"></a>00303                                  vbott, vtop, vleft, vright,
<a name="l00304"></a>00304                                  updated_sigma)
<a name="l00305"></a>00305 
<a name="l00306"></a>00306         <span class="keywordflow">return</span> (self.m_price_grid, self.m_time_grid, solu)
<a name="l00307"></a>00307 
<a name="l00308"></a>00308 
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